You're reading: Posts By David Benjamin

Sequences in the triangle and the fourth dimension

This is the second in a series of guest posts by David Benjamin, exploring the secrets of Pascal’s Triangle.

Sequences in the diagonals

There are many sequences of numbers to be found in Pascal’s triangle. The Natural numbers occur in the second diagonal, running in either direction, and the next two diagonals after that contain other important sequences:

Sequences in the diagonals

There are many sequences of numbers to be found in Pascal’s triangle. The Natural numbers occur in the second diagonal, running in either direction, and the next two diagonals after that contain other important sequences:

Pascal’s Triangle and its Secrets – Introduction

This is the first in a series of guest posts by David Benjamin, exploring the secrets of Pascal’s Triangle.

The triangle of Natural numbers below contains the first seven rows of what is called Pascal’s triangle. Each row begins and ends with the number 1, and each of the remaining numbers, from the third row onwards, is the sum of the two numbers ‘above’:

Pascal's triangle, with three triangles of numbers (two in one line, that sum to the one between them on the line below) highlighted in colour
The first seven rows of Pascal’s triangle, showing some pairs and their sums below (highlighted)
Animation showing numbers in Pascal's triangle being generated by adding the pair above
Generating the triangle

The extraordinary Cardano family

In this guest post by David Benjamin, we explore a little of the life and times of Girolamo Cardano and his interesting family.

Girolamo Cardano (1501- 1576) was at various times in his life a physician, mathematician, inventor, addictive gambler and prisoner. He was the illegitimate son of Fazio Cardano and Chiara Micheria, and the Cardano family was a dysfunctional 16th Century version of the Simpsons.

Google+